Bonding Forces and Energies on the Potential Energy Surface (PES) of the Optimized Gold Atomic Clusters at the Gradient (ds = 0.01 a.u.)

We have carried out the present ab initio study by using upto- date computational concepts through our newly developed Numerical Finite-Difference analysis via DFTB method. Significantly, to differentiate between zero (translational and rotational motion) and non-zero (vibrational motion) energy eigenvectors, we have accurately predicted the gradient ds=0.01 a.u. at the Potential Energy Surface (PES) of the re-optimized gold atomic structures Au 3-58 at ΔE = 0. With this small energy gap, we can see how the interaction of the different atomic motions was varied with 3N and 3N-6 degrees of freedom, and also they are very independent to each other in gold atomic clusters. Moreover, the non-zero eigenvalues are quite stable whereas the values of the zero-eigen values are varying over several orders of magnitude. Keywords: Gold Atomic Clusters; Density-Functional Tight- Binding (DFTB) approach; Finite-Difference Method; Force Constants (FCs); Energy Eigen Vector